Contrast post-hoc test on non-significant factor levels

Question

Is it meaningful to interpret the contrast result from a post-hoc test on factor levels that have non-significant coefficients in the fitted mixed model regression?

I'm using a contrast test using emmeans package to see if there is any significant difference between the treatment groups in my analysis. But the contrast test on a couple of factor levels does not make sense (I don't go to the details)! These are the factor levels that had non-significant coefficients in my GLMM model. I couldn't find any reason for it. So, my question is whether interpreting post-hoc test is meaningful when the coefficients are not significant. And should I ignore those factor levels??

Edits:

Here is the fitted model:

library(rstanarm)
library(emmeans)

fit1 <- stan_glmer(Response ~ 1 + Treatment + Time + (1 | Replicate),
                   family = binomial(link = "logit"),
                   cores = getOption("mc.cores", 4L),
                   data = mydata)

# calculating the mean differences
emm2 <- emmeans(fit1, specs = pairwise ~ Treatment | Time)

These are the coefficient estimates and the contrast results. The part that does not make sense is the difference between the proportion of the response in the Treat1 and Treat3 is much higher than those from the Treat2. But the Treat2 has a significant contrast with both Treat1 and Treat3, while the Treat1-Treat3 contrast is non-significant. If you notice, both Treat1 and Treat2 have also non-significant coefficients in the original mixed model.

Answer 1

It is certainly meaningful. The specific contrasts have exactly the same meaning, regardless of whether the overall test is significant or not, or even whether you do a main test at all.

Of course, doing multiple tests increases your type 1 error. But, then, it decreases your type 2 error (most things that increase one decrease the other). In some cases, type 2 errors are much worse than type 1.

And you have to be honest about what you did when you report it.

Answer 2

For your specific question : it is not meaningful in general to interpret posthoc result if the omnibus test is not significant. You are increasing your type I error rate, misspecifying your data, as well as violating your main hypothesis. However, it can be meaningful if the posthoc analysis answers a specific a priori hypothesis. It has to be carried adequately though.